Already known from document EP-A 780 884 is a reflector lamp with two-pin base, in the case of which a resilient lamp support fitted on the bulb is fitted transverse to the reflector axis and rests on an annularly circumferential step in the reflector neck. The lamp support is fastened in the reflector under biasing. U.S. Pat. No. 5,466,981 discloses a reflector lamp with a screw base and with a resilient lamp support. Fitted in the reflector neck are a plurality of circumferential steps, with the result that the same spherical cap can be used for bulbs and lamp supports of different size.